Poisson Hypothesis for Information Networks II. Cases of Violations and Phase Transitions

TL;DR

This paper investigates queuing networks that defy equilibrium, using non-linear Markov processes to demonstrate non-ergodic behavior and eternal transience, revealing phase transitions and violations of the Poisson hypothesis.

Contribution

It introduces specific non-linear Markov process models showing non-ergodic behavior and phase transitions in information networks, challenging existing assumptions.

Findings

Networks exhibit eternal transience without reaching equilibrium

Construction of non-ergodic non-linear Markov processes

Identification of phase transitions in network behavior

Abstract

We present examples of queuing networks that never come to equilibrium. That is achieved by constructing Non-linear Markov Processes, which are non-ergodic, and possess eternal transience property.